A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...

This paper is concerned with approximation properties of orthonormal mapped Chebyshev functions (OMCFs) in unbounded domains. Unlike the usual mapped Chebyshev functions which are associated with weighted Sobolev spaces, the OMCFs are associated with the usual (non-weighted) Sobolev spaces. This leads to particularly simple stiffness and mass matrices for higher-dimensional problems. The approx...

We consider the β-expansion of 1 which encodes a rational rotation on R/Z under a certain partition. Via transforming its βpolynomial into a linear combination of Chebyshev polynomials, we specify the minimal polynomial of β over the field of rationals. At the end, some number theoretical conjectures are posed with computational evidence to support them.

We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.

In this article, we prove that every unicritical polynomial map has only rational multipliers is either a power or Chebyshev map. This provides some evidence in support of conjecture by Milnor concerning maps whose are all integers.

Let [Formula: see text] be an odd natural number. In 1738, Abraham de Moivre introduced a family of polynomials degree with rational coefficients, all which are solvable. So far, the Galois groups these have been investigated only for prime numbers and under special assumptions. We describe arbitrary in irreducible case, up to few exceptions. addition, we express zeros such polynomial as functi...